Media flows have been classified into streaming flows and elastic flows. Traditionally, admission control schemes, in middleware systems and otherwise, have dealt with streaming flows. In the Internet context, elastic TCP flows have been considered for admission control more recently -- the aim being to ensure that they actually complete. In this paper, we present a simple reservation-based abstraction for middleware systems: an elastic flow with deadlines, that includes streaming flows as a special case. We use this specification in a simple model of a link. We then present a novel way to view the problem, as a maximum network flow problem. We show that this formulation also provides an admissible schedule for the flows. We then study the incremental version of the admission control problem, and present some heuristics. We finally briefly explore potential applications of this abstraction.